Question: The following line passes through point $(-7, 9)$ : $y = -\dfrac{3}{4} x + b$ What is the value of the $y$ -intercept $b$ ?
Explanation: Substituting $(-7, 9)$ into the equation gives: $9 = -\dfrac{3}{4} \cdot -7 + b$ $9 = \dfrac{21}{4} + b$ $b = 9 - \dfrac{21}{4}$ $b = \dfrac{15}{4}$ Plugging in $\dfrac{15}{4}$ for $b$, we get $y = -\dfrac{3}{4} x + \dfrac{15}{4}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(-7, 9)$